Analytical solution of 1-dimensional peridynamic equation of motion

Tools

Yang, Zhenghao and Ma, Chien-Ching and Oterkus, Erkan and Oterkus, Selda and Naumenko, Konstantin (2023) Analytical solution of 1-dimensional peridynamic equation of motion. Journal of Peridynamics and Nonlocal Modeling, 5. 356–374. ISSN 2522-8978 (https://doi.org/10.1007/s42102-022-00086-1)

[thumbnail of Yang-etal-JPNM-2022-Analytical-solution-of-1-dimensional-peridynamic-equation]
Preview
 Text. Filename: Yang_etal_JPNM_2022_Analytical_solution_of_1_dimensional_peridynamic_equation.pdf
Accepted Author Manuscript
License: Strathprints license 1.0
Download (3MB)| Preview

Abstract

Peridynamics has been introduced to overcome limitations of classical continuum mechanics. Peridynamic equations of motion are in the form of integro-differential equations and analytical solutions of these equations are limited in the literature. In this study, a new analytical solution methodology for 1-Dimensional peridynamic equation of motion is presented by utilising inverse Fourier Transform. Analytical solutions for both static and dynamic conditions are obtained. Moreover, different boundary conditions including fixedfixed and fixed-free are considered. Several numerical cases are demonstrated to show the capability of the presented methodology and peridynamic results are compared against results obtained from classical continuum mechanics. A very good agreement between these two different approaches is observed which shows the capability of the current approach.

ORCID iDs

Yang, Zhenghao, Ma, Chien-Ching, Oterkus, Erkan ORCID logoORCID: https://orcid.org/0000-0002-4614-7214, Oterkus, Selda ORCID logoORCID: https://orcid.org/0000-0003-0474-0279 and Naumenko, Konstantin;
CORE (COnnecting REpositories)